Figure 4.37 shows two forces, and , acting on a spacecraft; the plus signs indicate that the forces are directed along the +x axis. A third force also acts on the spacecraft but is not shown in the drawing. The craft is moving with a constant velocity of +850 m/s. Find the magnitude and direction of .

Figure 4.37    Two horizontal forces, and , act on the spacecraft. A third force also acts but is not shown.

Concept Questions and Answers Suppose the spacecraft were stationary. What would be the direction of ? Answer: If the spacecraft were stationary, its acceleration would be zero. According to Newton's second law, the acceleration of an object is proportional to the net force acting on it. Thus, the net force must also be zero. But the net force is the vector sum of the three forces in this case. Therefore, the force must have a direction such that it balances to zero the forces and . Since and point along the +x axis in Figure 4.37, must then point along the -x axis. When the spacecraft is moving at a constant velocity of +850 m/s, what is the direction of ? Answer: Since the velocity is constant, the acceleration is still zero. As a result, everything we said in the stationary case applies again here. The net force is zero, and the force must point along the -x axis in Figure 4.37.

Solution   Since the velocity is constant, the acceleration is zero. The net force must also be zero, so that Solving for F₃ yields The minus sign in the answer means that points opposite to the sum of and , or along the -x axis in Figure 4.37. The force has a magnitude of 8000 N, which is the magnitude of the sum of the forces and . The answer is independent of the velocity of the spacecraft, as long as that velocity remains constant.